Hybrid Parallel Tempering and Simulated Annealing Method

In this paper, we propose a new hybrid scheme of parallel tempering and simulated annealing (hybrid PT/SA). Within the hybrid PT/SA scheme, a composite system with multiple conformations is evolving in parallel on a temperature ladder with various transition step sizes. The simulated annealing (SA) process uses a cooling scheme to decrease the temperature values in the temperature ladder to the target temperature. The parallel tempering (PT) scheme is employed to reduce the equilibration relaxation time of the composite system at a particular temperature ladder configuration in the SA process. The hybrid PT/SA method reduces the waiting time in deep local minima and thus leads to a more efficient sampling capability on high-dimensional complicated objective function landscapes. Compared to the approaches PT and parallel SA with the same temperature ladder, transition step sizes, and cooling scheme (parallel SA) configurations, our preliminary results obtained with the hybrid PT/SA method confirm the expected improvements in simulations of several test objective functions, including the Rosenbrock’s function and the “rugged” funnel-like function, and several instantiations of the traveling salesman problem. The hybrid PT/SA may have slower convergence than genetic algorithms (GA) with good crossover heuristics, but it has the advantage of tolerating “bad” initial values and displaying robust sampling capability, even in the absence of additional information. Moreover, the hybrid PT/SA has natural parallelization potential.